Building a base for my wood stove

I am researching updating my old wood stove which is nowhere near fire code (and therefore not being used). The problem was it was installed too close to the walls and the only thing between it and the carpeted (indoor/outdoor) floor was some loosely placed bricks.

The stove requires about 36 inches of clearance from the sides and 32 from the rear. Its in a corner where its about 20 inches to the wall at the closest point. From what I read here, Durock cement board seems to be a great fix. With the board installed over the two walls around the stove, it will cut the minimal install distance to 12 inches, more than I currently need.

The second part is getting the stove base up to snuff. I plan to screw a proper sized piece of plywood directly over the existing carpet, followed by a piece of 1/2" Durock attached as indicated in the above link. On top of that I will add some ceramic tiles and wood trim around the whole base.

My question is has anyone had experience using Durock for this purpose and are there any issues to worry about regarding ceramic tile for a wood stove base? I'm also unsure of whether to remove the carpeting under the base or just build over it.